No they don't but I can see why you might think that.

ePassports (the ones with the stylised "chip" image on the cover) do have X.509 certificates baked into them. And ePassports do say "We are the government, and this is Jeff" (if you are Jeff) but that's not what the X.509 certificate says.

Each X.509 certificate is one of a relatively small number minted by your government which says "We are the government of country X and this is a public document signing key".

Then the passports all contain raw data (such as a photograph and summary information about their subject) with this certificate and a signature over the raw passport data that can be authenticated with the public signing key.

So there's an X.509 certificate but it isn't for Jeff, and there's data about Jeff, but it isn't in an X.509 certificate.